Question

A wheel 30 cm in diameter accelerates uniformly from 245 rpm to 380 rpm in 6.1 s . Part A How far will a point on the edge of the wheel have traveled in this time

Answer 1

A point on the edge of the wheel will travel 199.563 radians at the given time.

Step-by-step explanation:

Given;

initial angular velocity of the wheel;
`\omega _i = 245 \ rev/\min = 245\ (rev)/(\min) * (2\pi)/(1\ rev) * (1 \ \min)/(60 \ s) = 25.66 \ rad/s`

final angular velocity of the wheel;

`\omega _f = 380 \ rev/\min = 380 \ (rev)/(\min) * (2\pi)/(1\ rev) * (1 \ \min)/(60 \ s) = 39.80 \ rad/s`

radius of the wheel, d/2 = (30 cm ) / 2 = 15 cm = 0.15 m

time of motion, t = 6.1 s

The angular distance traveled by the edge of the wheel is calculated as;

`\theta = ((\omega_f + \omega_i)/(2) )t\\\\\theta = ((39.8 + 25.66)/(2) )* 6.1\\\\\theta = 199.653 \ radian`

Therefore, a point on the edge of the wheel will travel 199.563 radians at the given time.